HOMEWORK 8 1. Calculate the flux ff Finds when F = mp/p', with p= zi + yj + zk, p? = a? + y' + 23, and S is a sphere centered at the origin. Perform the same calculation when S is a cube centered at the origin. Hint: The divergence theorem cannot be applied at p = 0 because F is infinite at that location. 2. A spherical pellet of radius a that is heated uniformly (per unit volume) by a chemical reaction has the equilibrium temperature distribution where Q is the rate at which heat energy is added per unit volume, k is the coefficient of thermal conductivity and p' = 12 + y' + 22. The heat flux is given by q = -kVT. Compute the total amount of heat flux out of the sphere using a surface integral and show that this is equal to the rate at which heat energy is being added to the entire sphere. 3. Evaluate [( + z +3)ds where S is given by portion of the plane z = a + y satisfying a + y?